UnivariateLaurentSeries(Coef, var, cen)ΒΆ

laurent.spad line 520

Dense Laurent series in one variable UnivariateLaurentSeries is a domain representing Laurent series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring, the power series variable, and the center of the power series expansion. For example, UnivariateLaurentSeries(Integer, x, 3) represents Laurent series in (x - 3) with integer coefficients.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (%, Coef) -> %
from RightModule Coef
*: (%, Fraction Integer) -> % if Coef has Algebra Fraction Integer
from RightModule Fraction Integer
*: (%, UnivariateTaylorSeries(Coef, var, cen)) -> % if Coef has Field
from RightModule UnivariateTaylorSeries(Coef, var, cen)
*: (Coef, %) -> %
from LeftModule Coef
*: (Fraction Integer, %) -> % if Coef has Algebra Fraction Integer
from LeftModule Fraction Integer
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
*: (UnivariateTaylorSeries(Coef, var, cen), %) -> % if Coef has Field
from LeftModule UnivariateTaylorSeries(Coef, var, cen)
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
/: (%, %) -> % if Coef has Field
from Field
/: (%, Coef) -> % if Coef has Field
from AbelianMonoidRing(Coef, Integer)
/: (UnivariateTaylorSeries(Coef, var, cen), UnivariateTaylorSeries(Coef, var, cen)) -> % if Coef has Field
from QuotientFieldCategory UnivariateTaylorSeries(Coef, var, cen)
<: (%, %) -> Boolean if UnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field
from PartialOrder
<=: (%, %) -> Boolean if UnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field
from PartialOrder
=: (%, %) -> Boolean
from BasicType
>: (%, %) -> Boolean if UnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field
from PartialOrder
>=: (%, %) -> Boolean if UnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field
from PartialOrder
^: (%, %) -> % if Coef has Algebra Fraction Integer
from ElementaryFunctionCategory
^: (%, Fraction Integer) -> % if Coef has Algebra Fraction Integer
from RadicalCategory
^: (%, Integer) -> % if Coef has Field
from DivisionRing
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
abs: % -> % if UnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field
from OrderedRing
acos: % -> % if Coef has Algebra Fraction Integer
from ArcTrigonometricFunctionCategory
acosh: % -> % if Coef has Algebra Fraction Integer
from ArcHyperbolicFunctionCategory
acot: % -> % if Coef has Algebra Fraction Integer
from ArcTrigonometricFunctionCategory
acoth: % -> % if Coef has Algebra Fraction Integer
from ArcHyperbolicFunctionCategory
acsc: % -> % if Coef has Algebra Fraction Integer
from ArcTrigonometricFunctionCategory
acsch: % -> % if Coef has Algebra Fraction Integer
from ArcHyperbolicFunctionCategory
annihilate?: (%, %) -> Boolean
from Rng
antiCommutator: (%, %) -> %
from NonAssociativeSemiRng
approximate: (%, Integer) -> Coef if Coef has coerce: Symbol -> Coef and Coef has ^: (Coef, Integer) -> Coef
from UnivariatePowerSeriesCategory(Coef, Integer)
asec: % -> % if Coef has Algebra Fraction Integer
from ArcTrigonometricFunctionCategory
asech: % -> % if Coef has Algebra Fraction Integer
from ArcHyperbolicFunctionCategory
asin: % -> % if Coef has Algebra Fraction Integer
from ArcTrigonometricFunctionCategory
asinh: % -> % if Coef has Algebra Fraction Integer
from ArcHyperbolicFunctionCategory
associates?: (%, %) -> Boolean if Coef has IntegralDomain
from EntireRing
associator: (%, %, %) -> %
from NonAssociativeRng
atan: % -> % if Coef has Algebra Fraction Integer
from ArcTrigonometricFunctionCategory
atanh: % -> % if Coef has Algebra Fraction Integer
from ArcHyperbolicFunctionCategory
ceiling: % -> UnivariateTaylorSeries(Coef, var, cen) if UnivariateTaylorSeries(Coef, var, cen) has IntegerNumberSystem and Coef has Field
from QuotientFieldCategory UnivariateTaylorSeries(Coef, var, cen)
center: % -> Coef
from UnivariatePowerSeriesCategory(Coef, Integer)
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
charthRoot: % -> Union(%, failed) if Coef has CharacteristicNonZero or % has CharacteristicNonZero and UnivariateTaylorSeries(Coef, var, cen) has PolynomialFactorizationExplicit and Coef has Field or UnivariateTaylorSeries(Coef, var, cen) has CharacteristicNonZero and Coef has Field
from CharacteristicNonZero
coefficient: (%, Integer) -> Coef
from AbelianMonoidRing(Coef, Integer)
coerce: % -> % if Coef has CommutativeRing
from Algebra %
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Coef -> % if Coef has CommutativeRing
from Algebra Coef
coerce: Fraction Integer -> % if Coef has Algebra Fraction Integer
from Algebra Fraction Integer
coerce: Integer -> %
from NonAssociativeRing
coerce: Symbol -> % if UnivariateTaylorSeries(Coef, var, cen) has RetractableTo Symbol and Coef has Field
from RetractableTo Symbol
coerce: UnivariateTaylorSeries(Coef, var, cen) -> %
from UnivariateLaurentSeriesConstructorCategory(Coef, UnivariateTaylorSeries(Coef, var, cen))
coerce: Variable var -> %
coerce(var) converts the series variable var into a Laurent series.
commutator: (%, %) -> %
from NonAssociativeRng
complete: % -> %
from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and UnivariateTaylorSeries(Coef, var, cen) has PolynomialFactorizationExplicit and Coef has Field
from PolynomialFactorizationExplicit
convert: % -> DoubleFloat if UnivariateTaylorSeries(Coef, var, cen) has RealConstant and Coef has Field
from ConvertibleTo DoubleFloat
convert: % -> Float if UnivariateTaylorSeries(Coef, var, cen) has RealConstant and Coef has Field
from ConvertibleTo Float
convert: % -> InputForm if UnivariateTaylorSeries(Coef, var, cen) has ConvertibleTo InputForm and Coef has Field
from ConvertibleTo InputForm
convert: % -> Pattern Float if UnivariateTaylorSeries(Coef, var, cen) has ConvertibleTo Pattern Float and Coef has Field
from ConvertibleTo Pattern Float
convert: % -> Pattern Integer if UnivariateTaylorSeries(Coef, var, cen) has ConvertibleTo Pattern Integer and Coef has Field
from ConvertibleTo Pattern Integer
cos: % -> % if Coef has Algebra Fraction Integer
from TrigonometricFunctionCategory
cosh: % -> % if Coef has Algebra Fraction Integer
from HyperbolicFunctionCategory
cot: % -> % if Coef has Algebra Fraction Integer
from TrigonometricFunctionCategory
coth: % -> % if Coef has Algebra Fraction Integer
from HyperbolicFunctionCategory
csc: % -> % if Coef has Algebra Fraction Integer
from TrigonometricFunctionCategory
csch: % -> % if Coef has Algebra Fraction Integer
from HyperbolicFunctionCategory
D: % -> % if Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has DifferentialRing and Coef has Field
from DifferentialRing
D: (%, List Symbol) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field
from PartialDifferentialRing Symbol
D: (%, List Symbol, List NonNegativeInteger) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field
from PartialDifferentialRing Symbol
D: (%, NonNegativeInteger) -> % if Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has DifferentialRing and Coef has Field
from DifferentialRing
D: (%, Symbol) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field
from PartialDifferentialRing Symbol
D: (%, Symbol, NonNegativeInteger) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field
from PartialDifferentialRing Symbol
D: (%, UnivariateTaylorSeries(Coef, var, cen) -> UnivariateTaylorSeries(Coef, var, cen)) -> % if Coef has Field
from DifferentialExtension UnivariateTaylorSeries(Coef, var, cen)
D: (%, UnivariateTaylorSeries(Coef, var, cen) -> UnivariateTaylorSeries(Coef, var, cen), NonNegativeInteger) -> % if Coef has Field
from DifferentialExtension UnivariateTaylorSeries(Coef, var, cen)
degree: % -> Integer
from UnivariateLaurentSeriesConstructorCategory(Coef, UnivariateTaylorSeries(Coef, var, cen))
denom: % -> UnivariateTaylorSeries(Coef, var, cen) if Coef has Field
from QuotientFieldCategory UnivariateTaylorSeries(Coef, var, cen)
denominator: % -> % if Coef has Field
from QuotientFieldCategory UnivariateTaylorSeries(Coef, var, cen)
differentiate: % -> % if Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has DifferentialRing and Coef has Field
from DifferentialRing
differentiate: (%, List Symbol) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field
from PartialDifferentialRing Symbol
differentiate: (%, List Symbol, List NonNegativeInteger) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field
from PartialDifferentialRing Symbol
differentiate: (%, NonNegativeInteger) -> % if Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has DifferentialRing and Coef has Field
from DifferentialRing
differentiate: (%, Symbol) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field
from PartialDifferentialRing Symbol
differentiate: (%, Symbol, NonNegativeInteger) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field
from PartialDifferentialRing Symbol
differentiate: (%, UnivariateTaylorSeries(Coef, var, cen) -> UnivariateTaylorSeries(Coef, var, cen)) -> % if Coef has Field
from DifferentialExtension UnivariateTaylorSeries(Coef, var, cen)
differentiate: (%, UnivariateTaylorSeries(Coef, var, cen) -> UnivariateTaylorSeries(Coef, var, cen), NonNegativeInteger) -> % if Coef has Field
from DifferentialExtension UnivariateTaylorSeries(Coef, var, cen)
differentiate: (%, Variable var) -> %
differentiate(f(x), x) returns the derivative of f(x) with respect to x.
divide: (%, %) -> Record(quotient: %, remainder: %) if Coef has Field
from EuclideanDomain
elt: (%, %) -> %
from Eltable(%, %)
elt: (%, Integer) -> Coef
from UnivariatePowerSeriesCategory(Coef, Integer)
elt: (%, UnivariateTaylorSeries(Coef, var, cen)) -> % if UnivariateTaylorSeries(Coef, var, cen) has Eltable(UnivariateTaylorSeries(Coef, var, cen), UnivariateTaylorSeries(Coef, var, cen)) and Coef has Field
from Eltable(UnivariateTaylorSeries(Coef, var, cen), %)
euclideanSize: % -> NonNegativeInteger if Coef has Field
from EuclideanDomain
eval: (%, Coef) -> Stream Coef if Coef has ^: (Coef, Integer) -> Coef
from UnivariatePowerSeriesCategory(Coef, Integer)
eval: (%, Equation UnivariateTaylorSeries(Coef, var, cen)) -> % if UnivariateTaylorSeries(Coef, var, cen) has Evalable UnivariateTaylorSeries(Coef, var, cen) and Coef has Field
from Evalable UnivariateTaylorSeries(Coef, var, cen)
eval: (%, List Equation UnivariateTaylorSeries(Coef, var, cen)) -> % if UnivariateTaylorSeries(Coef, var, cen) has Evalable UnivariateTaylorSeries(Coef, var, cen) and Coef has Field
from Evalable UnivariateTaylorSeries(Coef, var, cen)
eval: (%, List Symbol, List UnivariateTaylorSeries(Coef, var, cen)) -> % if UnivariateTaylorSeries(Coef, var, cen) has InnerEvalable(Symbol, UnivariateTaylorSeries(Coef, var, cen)) and Coef has Field
from InnerEvalable(Symbol, UnivariateTaylorSeries(Coef, var, cen))
eval: (%, List UnivariateTaylorSeries(Coef, var, cen), List UnivariateTaylorSeries(Coef, var, cen)) -> % if UnivariateTaylorSeries(Coef, var, cen) has Evalable UnivariateTaylorSeries(Coef, var, cen) and Coef has Field
from InnerEvalable(UnivariateTaylorSeries(Coef, var, cen), UnivariateTaylorSeries(Coef, var, cen))
eval: (%, Symbol, UnivariateTaylorSeries(Coef, var, cen)) -> % if UnivariateTaylorSeries(Coef, var, cen) has InnerEvalable(Symbol, UnivariateTaylorSeries(Coef, var, cen)) and Coef has Field
from InnerEvalable(Symbol, UnivariateTaylorSeries(Coef, var, cen))
eval: (%, UnivariateTaylorSeries(Coef, var, cen), UnivariateTaylorSeries(Coef, var, cen)) -> % if UnivariateTaylorSeries(Coef, var, cen) has Evalable UnivariateTaylorSeries(Coef, var, cen) and Coef has Field
from InnerEvalable(UnivariateTaylorSeries(Coef, var, cen), UnivariateTaylorSeries(Coef, var, cen))
exp: % -> % if Coef has Algebra Fraction Integer
from ElementaryFunctionCategory
expressIdealMember: (List %, %) -> Union(List %, failed) if Coef has Field
from PrincipalIdealDomain
exquo: (%, %) -> Union(%, failed) if Coef has IntegralDomain
from EntireRing
extend: (%, Integer) -> %
from UnivariatePowerSeriesCategory(Coef, Integer)
extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %) if Coef has Field
from EuclideanDomain
extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed) if Coef has Field
from EuclideanDomain
factor: % -> Factored % if Coef has Field
from UniqueFactorizationDomain
factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UnivariateTaylorSeries(Coef, var, cen) has PolynomialFactorizationExplicit and Coef has Field
from PolynomialFactorizationExplicit
factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UnivariateTaylorSeries(Coef, var, cen) has PolynomialFactorizationExplicit and Coef has Field
from PolynomialFactorizationExplicit
floor: % -> UnivariateTaylorSeries(Coef, var, cen) if UnivariateTaylorSeries(Coef, var, cen) has IntegerNumberSystem and Coef has Field
from QuotientFieldCategory UnivariateTaylorSeries(Coef, var, cen)
fractionPart: % -> % if UnivariateTaylorSeries(Coef, var, cen) has EuclideanDomain and Coef has Field
from QuotientFieldCategory UnivariateTaylorSeries(Coef, var, cen)
gcd: (%, %) -> % if Coef has Field
from GcdDomain
gcd: List % -> % if Coef has Field
from GcdDomain
gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has Field
from GcdDomain
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
init: % if UnivariateTaylorSeries(Coef, var, cen) has StepThrough and Coef has Field
from StepThrough
integrate: % -> % if Coef has Algebra Fraction Integer
from UnivariateLaurentSeriesCategory Coef
integrate: (%, Symbol) -> % if Coef has AlgebraicallyClosedFunctionSpace Integer and Coef has Algebra Fraction Integer and Coef has TranscendentalFunctionCategory and Coef has PrimitiveFunctionCategory or Coef has Algebra Fraction Integer and Coef has integrate: (Coef, Symbol) -> Coef and Coef has variables: Coef -> List Symbol
from UnivariateLaurentSeriesCategory Coef
integrate: (%, Variable var) -> % if Coef has Algebra Fraction Integer
integrate(f(x)) returns an anti-derivative of the power series f(x) with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.
inv: % -> % if Coef has Field
from DivisionRing
latex: % -> String
from SetCategory
laurent: (Integer, Stream Coef) -> %
from UnivariateLaurentSeriesCategory Coef
laurent: (Integer, UnivariateTaylorSeries(Coef, var, cen)) -> %
from UnivariateLaurentSeriesConstructorCategory(Coef, UnivariateTaylorSeries(Coef, var, cen))
lcm: (%, %) -> % if Coef has Field
from GcdDomain
lcm: List % -> % if Coef has Field
from GcdDomain
lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %) if Coef has Field
from LeftOreRing
leadingCoefficient: % -> Coef
from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
leadingMonomial: % -> %
from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
log: % -> % if Coef has Algebra Fraction Integer
from ElementaryFunctionCategory
map: (Coef -> Coef, %) -> %
from AbelianMonoidRing(Coef, Integer)
map: (UnivariateTaylorSeries(Coef, var, cen) -> UnivariateTaylorSeries(Coef, var, cen), %) -> % if Coef has Field
from FullyEvalableOver UnivariateTaylorSeries(Coef, var, cen)
max: (%, %) -> % if UnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field
from OrderedSet
min: (%, %) -> % if UnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field
from OrderedSet
monomial: (%, List SingletonAsOrderedSet, List Integer) -> %
from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
monomial: (%, SingletonAsOrderedSet, Integer) -> %
from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
monomial: (Coef, Integer) -> %
from AbelianMonoidRing(Coef, Integer)
monomial?: % -> Boolean
from AbelianMonoidRing(Coef, Integer)
multiEuclidean: (List %, %) -> Union(List %, failed) if Coef has Field
from EuclideanDomain
multiplyCoefficients: (Integer -> Coef, %) -> %
from UnivariateLaurentSeriesCategory Coef
multiplyExponents: (%, PositiveInteger) -> %
from UnivariatePowerSeriesCategory(Coef, Integer)
negative?: % -> Boolean if UnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field
from OrderedRing
nextItem: % -> Union(%, failed) if UnivariateTaylorSeries(Coef, var, cen) has StepThrough and Coef has Field
from StepThrough
nthRoot: (%, Integer) -> % if Coef has Algebra Fraction Integer
from RadicalCategory
numer: % -> UnivariateTaylorSeries(Coef, var, cen) if Coef has Field
from QuotientFieldCategory UnivariateTaylorSeries(Coef, var, cen)
numerator: % -> % if Coef has Field
from QuotientFieldCategory UnivariateTaylorSeries(Coef, var, cen)
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
order: % -> Integer
from UnivariatePowerSeriesCategory(Coef, Integer)
order: (%, Integer) -> Integer
from UnivariatePowerSeriesCategory(Coef, Integer)
patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if UnivariateTaylorSeries(Coef, var, cen) has PatternMatchable Float and Coef has Field
from PatternMatchable Float
patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if UnivariateTaylorSeries(Coef, var, cen) has PatternMatchable Integer and Coef has Field
from PatternMatchable Integer
pi: () -> % if Coef has Algebra Fraction Integer
from TranscendentalFunctionCategory
pole?: % -> Boolean
from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
positive?: % -> Boolean if UnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field
from OrderedRing
prime?: % -> Boolean if Coef has Field
from UniqueFactorizationDomain
principalIdeal: List % -> Record(coef: List %, generator: %) if Coef has Field
from PrincipalIdealDomain
quo: (%, %) -> % if Coef has Field
from EuclideanDomain
rationalFunction: (%, Integer) -> Fraction Polynomial Coef if Coef has IntegralDomain
from UnivariateLaurentSeriesCategory Coef
rationalFunction: (%, Integer, Integer) -> Fraction Polynomial Coef if Coef has IntegralDomain
from UnivariateLaurentSeriesCategory Coef
recip: % -> Union(%, failed)
from MagmaWithUnit
reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if UnivariateTaylorSeries(Coef, var, cen) has LinearlyExplicitOver Integer and Coef has Field
from LinearlyExplicitOver Integer
reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix UnivariateTaylorSeries(Coef, var, cen), vec: Vector UnivariateTaylorSeries(Coef, var, cen)) if Coef has Field
from LinearlyExplicitOver UnivariateTaylorSeries(Coef, var, cen)
reducedSystem: Matrix % -> Matrix Integer if UnivariateTaylorSeries(Coef, var, cen) has LinearlyExplicitOver Integer and Coef has Field
from LinearlyExplicitOver Integer
reducedSystem: Matrix % -> Matrix UnivariateTaylorSeries(Coef, var, cen) if Coef has Field
from LinearlyExplicitOver UnivariateTaylorSeries(Coef, var, cen)
reductum: % -> %
from AbelianMonoidRing(Coef, Integer)
rem: (%, %) -> % if Coef has Field
from EuclideanDomain
removeZeroes: % -> %
from UnivariateLaurentSeriesConstructorCategory(Coef, UnivariateTaylorSeries(Coef, var, cen))
removeZeroes: (Integer, %) -> %
from UnivariateLaurentSeriesConstructorCategory(Coef, UnivariateTaylorSeries(Coef, var, cen))
retract: % -> Fraction Integer if UnivariateTaylorSeries(Coef, var, cen) has RetractableTo Integer and Coef has Field
from RetractableTo Fraction Integer
retract: % -> Integer if UnivariateTaylorSeries(Coef, var, cen) has RetractableTo Integer and Coef has Field
from RetractableTo Integer
retract: % -> Symbol if UnivariateTaylorSeries(Coef, var, cen) has RetractableTo Symbol and Coef has Field
from RetractableTo Symbol
retract: % -> UnivariateTaylorSeries(Coef, var, cen)
from RetractableTo UnivariateTaylorSeries(Coef, var, cen)
retractIfCan: % -> Union(Fraction Integer, failed) if UnivariateTaylorSeries(Coef, var, cen) has RetractableTo Integer and Coef has Field
from RetractableTo Fraction Integer
retractIfCan: % -> Union(Integer, failed) if UnivariateTaylorSeries(Coef, var, cen) has RetractableTo Integer and Coef has Field
from RetractableTo Integer
retractIfCan: % -> Union(Symbol, failed) if UnivariateTaylorSeries(Coef, var, cen) has RetractableTo Symbol and Coef has Field
from RetractableTo Symbol
retractIfCan: % -> Union(UnivariateTaylorSeries(Coef, var, cen), failed)
from RetractableTo UnivariateTaylorSeries(Coef, var, cen)
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
sample: %
from AbelianMonoid
sec: % -> % if Coef has Algebra Fraction Integer
from TrigonometricFunctionCategory
sech: % -> % if Coef has Algebra Fraction Integer
from HyperbolicFunctionCategory
series: Stream Record(k: Integer, c: Coef) -> %
from UnivariateLaurentSeriesCategory Coef
sign: % -> Integer if UnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field
from OrderedRing
sin: % -> % if Coef has Algebra Fraction Integer
from TrigonometricFunctionCategory
sinh: % -> % if Coef has Algebra Fraction Integer
from HyperbolicFunctionCategory
sizeLess?: (%, %) -> Boolean if Coef has Field
from EuclideanDomain
smaller?: (%, %) -> Boolean if UnivariateTaylorSeries(Coef, var, cen) has Comparable and Coef has Field
from Comparable
solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if UnivariateTaylorSeries(Coef, var, cen) has PolynomialFactorizationExplicit and Coef has Field
from PolynomialFactorizationExplicit
sqrt: % -> % if Coef has Algebra Fraction Integer
from RadicalCategory
squareFree: % -> Factored % if Coef has Field
from UniqueFactorizationDomain
squareFreePart: % -> % if Coef has Field
from UniqueFactorizationDomain
squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UnivariateTaylorSeries(Coef, var, cen) has PolynomialFactorizationExplicit and Coef has Field
from PolynomialFactorizationExplicit
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
tan: % -> % if Coef has Algebra Fraction Integer
from TrigonometricFunctionCategory
tanh: % -> % if Coef has Algebra Fraction Integer
from HyperbolicFunctionCategory
taylor: % -> UnivariateTaylorSeries(Coef, var, cen)
from UnivariateLaurentSeriesConstructorCategory(Coef, UnivariateTaylorSeries(Coef, var, cen))
taylorIfCan: % -> Union(UnivariateTaylorSeries(Coef, var, cen), failed)
from UnivariateLaurentSeriesConstructorCategory(Coef, UnivariateTaylorSeries(Coef, var, cen))
taylorRep: % -> UnivariateTaylorSeries(Coef, var, cen)
from UnivariateLaurentSeriesConstructorCategory(Coef, UnivariateTaylorSeries(Coef, var, cen))
terms: % -> Stream Record(k: Integer, c: Coef)
from UnivariatePowerSeriesCategory(Coef, Integer)
truncate: (%, Integer) -> %
from UnivariatePowerSeriesCategory(Coef, Integer)
truncate: (%, Integer, Integer) -> %
from UnivariatePowerSeriesCategory(Coef, Integer)
unit?: % -> Boolean if Coef has IntegralDomain
from EntireRing
unitCanonical: % -> % if Coef has IntegralDomain
from EntireRing
unitNormal: % -> Record(unit: %, canonical: %, associate: %) if Coef has IntegralDomain
from EntireRing
variable: % -> Symbol
from UnivariatePowerSeriesCategory(Coef, Integer)
variables: % -> List SingletonAsOrderedSet
from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
wholePart: % -> UnivariateTaylorSeries(Coef, var, cen) if UnivariateTaylorSeries(Coef, var, cen) has EuclideanDomain and Coef has Field
from QuotientFieldCategory UnivariateTaylorSeries(Coef, var, cen)
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(Coef, Integer)

AbelianSemiGroup

Algebra % if Coef has CommutativeRing

Algebra Coef if Coef has CommutativeRing

Algebra Fraction Integer if Coef has Algebra Fraction Integer

Algebra UnivariateTaylorSeries(Coef, var, cen) if Coef has Field

ArcHyperbolicFunctionCategory if Coef has Algebra Fraction Integer

ArcTrigonometricFunctionCategory if Coef has Algebra Fraction Integer

BasicType

BiModule(%, %)

BiModule(Coef, Coef)

BiModule(Fraction Integer, Fraction Integer) if Coef has Algebra Fraction Integer

BiModule(UnivariateTaylorSeries(Coef, var, cen), UnivariateTaylorSeries(Coef, var, cen)) if Coef has Field

CancellationAbelianMonoid

canonicalsClosed if Coef has Field

canonicalUnitNormal if Coef has Field

CharacteristicNonZero if Coef has CharacteristicNonZero or UnivariateTaylorSeries(Coef, var, cen) has CharacteristicNonZero and Coef has Field

CharacteristicZero if Coef has CharacteristicZero or UnivariateTaylorSeries(Coef, var, cen) has CharacteristicZero and Coef has Field

CoercibleTo OutputForm

CommutativeRing if Coef has CommutativeRing

CommutativeStar if Coef has CommutativeRing

Comparable if UnivariateTaylorSeries(Coef, var, cen) has Comparable and Coef has Field

ConvertibleTo DoubleFloat if UnivariateTaylorSeries(Coef, var, cen) has RealConstant and Coef has Field

ConvertibleTo Float if UnivariateTaylorSeries(Coef, var, cen) has RealConstant and Coef has Field

ConvertibleTo InputForm if UnivariateTaylorSeries(Coef, var, cen) has ConvertibleTo InputForm and Coef has Field

ConvertibleTo Pattern Float if UnivariateTaylorSeries(Coef, var, cen) has ConvertibleTo Pattern Float and Coef has Field

ConvertibleTo Pattern Integer if UnivariateTaylorSeries(Coef, var, cen) has ConvertibleTo Pattern Integer and Coef has Field

DifferentialExtension UnivariateTaylorSeries(Coef, var, cen) if Coef has Field

DifferentialRing if Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has DifferentialRing and Coef has Field

DivisionRing if Coef has Field

ElementaryFunctionCategory if Coef has Algebra Fraction Integer

Eltable(%, %)

Eltable(UnivariateTaylorSeries(Coef, var, cen), %) if UnivariateTaylorSeries(Coef, var, cen) has Eltable(UnivariateTaylorSeries(Coef, var, cen), UnivariateTaylorSeries(Coef, var, cen)) and Coef has Field

EntireRing if Coef has IntegralDomain

EuclideanDomain if Coef has Field

Evalable UnivariateTaylorSeries(Coef, var, cen) if UnivariateTaylorSeries(Coef, var, cen) has Evalable UnivariateTaylorSeries(Coef, var, cen) and Coef has Field

Field if Coef has Field

FullyEvalableOver UnivariateTaylorSeries(Coef, var, cen) if Coef has Field

FullyLinearlyExplicitOver UnivariateTaylorSeries(Coef, var, cen) if Coef has Field

FullyPatternMatchable UnivariateTaylorSeries(Coef, var, cen) if Coef has Field

GcdDomain if Coef has Field

HyperbolicFunctionCategory if Coef has Algebra Fraction Integer

InnerEvalable(Symbol, UnivariateTaylorSeries(Coef, var, cen)) if UnivariateTaylorSeries(Coef, var, cen) has InnerEvalable(Symbol, UnivariateTaylorSeries(Coef, var, cen)) and Coef has Field

InnerEvalable(UnivariateTaylorSeries(Coef, var, cen), UnivariateTaylorSeries(Coef, var, cen)) if UnivariateTaylorSeries(Coef, var, cen) has Evalable UnivariateTaylorSeries(Coef, var, cen) and Coef has Field

IntegralDomain if Coef has IntegralDomain

LeftModule %

LeftModule Coef

LeftModule Fraction Integer if Coef has Algebra Fraction Integer

LeftModule UnivariateTaylorSeries(Coef, var, cen) if Coef has Field

LeftOreRing if Coef has Field

LinearlyExplicitOver Integer if UnivariateTaylorSeries(Coef, var, cen) has LinearlyExplicitOver Integer and Coef has Field

LinearlyExplicitOver UnivariateTaylorSeries(Coef, var, cen) if Coef has Field

Magma

MagmaWithUnit

Module % if Coef has CommutativeRing

Module Coef if Coef has CommutativeRing

Module Fraction Integer if Coef has Algebra Fraction Integer

Module UnivariateTaylorSeries(Coef, var, cen) if Coef has Field

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if Coef has IntegralDomain

OrderedAbelianGroup if UnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field

OrderedAbelianMonoid if UnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field

OrderedAbelianSemiGroup if UnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field

OrderedCancellationAbelianMonoid if UnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field

OrderedIntegralDomain if UnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field

OrderedRing if UnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field

OrderedSet if UnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field

PartialDifferentialRing Symbol if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or UnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field

PartialOrder if UnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field

Patternable UnivariateTaylorSeries(Coef, var, cen) if Coef has Field

PatternMatchable Float if UnivariateTaylorSeries(Coef, var, cen) has PatternMatchable Float and Coef has Field

PatternMatchable Integer if UnivariateTaylorSeries(Coef, var, cen) has PatternMatchable Integer and Coef has Field

PolynomialFactorizationExplicit if UnivariateTaylorSeries(Coef, var, cen) has PolynomialFactorizationExplicit and Coef has Field

PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)

PrincipalIdealDomain if Coef has Field

QuotientFieldCategory UnivariateTaylorSeries(Coef, var, cen) if Coef has Field

RadicalCategory if Coef has Algebra Fraction Integer

RealConstant if UnivariateTaylorSeries(Coef, var, cen) has RealConstant and Coef has Field

RetractableTo Fraction Integer if UnivariateTaylorSeries(Coef, var, cen) has RetractableTo Integer and Coef has Field

RetractableTo Integer if UnivariateTaylorSeries(Coef, var, cen) has RetractableTo Integer and Coef has Field

RetractableTo Symbol if UnivariateTaylorSeries(Coef, var, cen) has RetractableTo Symbol and Coef has Field

RetractableTo UnivariateTaylorSeries(Coef, var, cen)

RightModule %

RightModule Coef

RightModule Fraction Integer if Coef has Algebra Fraction Integer

RightModule UnivariateTaylorSeries(Coef, var, cen) if Coef has Field

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough if UnivariateTaylorSeries(Coef, var, cen) has StepThrough and Coef has Field

TranscendentalFunctionCategory if Coef has Algebra Fraction Integer

TrigonometricFunctionCategory if Coef has Algebra Fraction Integer

UniqueFactorizationDomain if Coef has Field

unitsKnown

UnivariateLaurentSeriesCategory Coef

UnivariateLaurentSeriesConstructorCategory(Coef, UnivariateTaylorSeries(Coef, var, cen))

UnivariatePowerSeriesCategory(Coef, Integer)

VariablesCommuteWithCoefficients